Question: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{r^2 - 11r + 24}{r^2 - 2r - 3}$
First factor the expressions in the numerator and denominator. $ \dfrac{r^2 - 11r + 24}{r^2 - 2r - 3} = \dfrac{(r - 8)(r - 3)}{(r + 1)(r - 3)} $ Notice that the term $(r - 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r - 3)$ gives: $n = \dfrac{r - 8}{r + 1}$ Since we divided by $(r - 3)$, $r \neq 3$. $n = \dfrac{r - 8}{r + 1}; \space r \neq 3$